In space-filling models

Isosurfaces of electron density are obtained from the probability density isosurfaces for molecules described in Chapter 6. These are surfaces in three-dimensional space that include all the points at which has a particular value. The value of electron density chosen to define the isosurface is selected by some definite, though arbitrary, criterion. There is broad acceptance of a standard density of 0.002 el ao), where is the Bohr radius. This value is thought to best represent the sizes and shapes of molecules because it corresponds to the van der Waals atomic radii discussed earlier in the context of repulsive forces. These are the same dimensions depicted in space-filling models of molecules. 

Fig. 4.9 Crystallographic structure of bacteriorhodopsin (A, PDB 1C3W) [64]. Trp86, Trpl82, and Tyrl 85 are shown in space-filling model together with the retinal chromophore in stick (A) or space-filling (B) drawing.

Cis alkenes are less stable than their irons isomers because of nonbonded interaction strain between alkyl substituents on the same side of the double bond in the cis isomer, as can be seen in space-filling models of the cis and irons isomers of 2-butene. This is the same type of steric strain that results in the preference for equatorial methylcyclohexane over axial methylcyclohexane (Section 3.6B). 

The space filling model developed by Corey, Pauling, and Koltun is also known as the CPK model, or scale model [197], It shows the relative volume (size) of different elements or of different parts of a molecule (Figure 2-123d). The model is based on spheres that represent the "electron cloud . These atomic spheres can be determined from the van der Waals radii (see Section 2.10.1), which indicate the most stable distance between two atoms (non-bonded nuclei). Since the spheres are all drawn to the same scale, the relative size of the overlapping electron clouds of the atoms becomes evident. The connectivities between atoms, the bonds, are not visualized because they are located beneath the atom spheres and are not visible in a non-transparent display (see Section 2.10). In contrast to other models, the CPK model makes it possible to visualize a first impression of the extent of a molecule. 

The earliest ball and stick models were exactly that wooden balls in which holes were drilled to ac commodate dowels that connected the atoms Plastic versions including relatively inexpensive student sets became available in the 1960s and proved to be a valuable learning aid Precisely scaled stainless steel framework and plastic space filling models although relatively expensive were standard equipment in most research laboratories... 

FIGURE 2 18 Acetylene is a linear molecule as indicated in (a) the structural formula and (b) a space filling model... 

FIGURE 5 5 Ball and spoke and space filling models of as and trans 2 butene The space filling model shows the serious van der Waals strain between two of the hydrogens in as 2 butene The molecule ad justs by expanding those bond angles that increase the separation between the crowded atoms The combi nation of angle strain and van der Waals strain makes as 2 butene less stable than trans 2 butene... 

Examine the models of 1 3 butadiene in Figure 10 6 on Learn mg By Modeling and com pare space filling models of the s CIS and s trans confor mation... 

The compound shown is quite unreactive in Diels-Alder reactions Make a space filling model of it in the conformation required for the Diels-Alder reaction to see why... 

FIGURE 19 6 Space filling model of a micelle formed by association of car boxylate ions derived from a long chain carboxylic acid The hydrocarbon chains tend to be on the inside and the carboxylate ions on the surface where they are in contact with water mole cules and metal cations... 

FIGURE 28 5 (a) Tube and (b) space filling models of a DNA double helix The carbohydrate-phosphate backbone is on the out side and can be roughly traced in (b) by the red oxygen atoms The blue atoms belong to the purine and pyrimidine bases and he on the inside The base pairing is more clearly seen in (a)... 

SpartanView uses the word density to identify size density surfaces The size density surface is similar in size and shape to a space filling model... 

Fig. 2. X-ray structure of dearniaooxytociii (a) space-filling model (b) equivalent stick model. Numbers and amino acids refer to positions indicated in...

Figure 1 Chemical structure and space-filling representation of a phosphatidylcholine, DPPC. Different parts of the molecule are referred to by the labels at the left together the choline and phosphate are referred to as the headgroup, which is zwitteriomc. In the space-filling model, H atoms are white, O and P gray, and C black. (From Ref. 55.)...

Figure 5.24 Space-filling model (green) of the sialic acid binding domain of hemagglutinin with a bound inhibitor (red) Illustrating the different binding grooves. The sialic acid moiety of the Inhibitor binds in the central groove. A large hydrophobic substituent, Ri, at the Cz position of sialic acid binds in a hydrophobic channel that runs from the central groove to the bottom of the domain. (Adapted from S.J. Watowich et al.. Structure 2 719-731, 1994.)...

The binding model, suggested by Brian Matthews, is shown schematically in (a) with connected circles for the Ca positions, (b) A schematic diagram of the Cro dimer with different colors for the two subunits, (c) A schematic space-filling model of the dimer of Cro bound to a bent B-DNA molecule. The sugar-phosphate backbone of DNA is orange, and the bases ate yellow. Protein atoms are colored red, blue, green, and white, [(a) Adapted from D. Ohlendorf et al., /. Mol. Evol. 19 109-114, 1983. (c) Courtesy of Brian Matthews.]... 

Figure 14.2 Models of a collagen-like peptide with a mutation Gly to Ala in the middle of the peptide (orange). Each polypeptide chain is folded into a polyproline type II helix and three chains form a superhelix similar to part of the collagen molecule. The alanine side chain is accommodated inside the superhelix causing a slight change in the twist of the individual chains, (a) Space-filling model, (b) Ribbon diagram. Compare with Figure 14.1c for the change caused by the alanine substitution. (Adapted from J. Bella et al.. Science 266 75-81, 1994.)...

Figure 14.15 Stmcture of the SI fragment of chicken myosin as a Richardson diagram (a) and a space-filling model (b). The two light chains are shown in magenta and yellow. The heavy chain is colored according to three proteolytic fragments produced by trypsin a 25-kDa N-terminal domain (green) a central 50-kDa fragment (red) divided by a cleft into a 50K upper and a 50K lower domain and a 20-kDa C-terminal domain (blue) that links the myosin head to the coiled-coil tail. The 50-kDa and 20-kDa domains both bind actin, while the 25-kDa domain binds ATP. [(b) Courtesy of 1. Rayment.]...

As useful as molecular models are, they are limited in that they only show the location of the atoms and the space they occupy. Another important dimension to molecular structure is its electron distribution. We introduced electrostatic potential maps in Section 1.5 as a way of illustrating charge distribution and will continue to use them throughout the text. Figure 1.6(d) shows the electrostatic potential map of methane. Its overall shape is similar to the volume occupied by the space-filling model. The most electron-rich regions are closer to carbon and the most electron-poor ones are closer to the hydrogens. 

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